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AST 113 – Summer 2009 Extrasolar Planets
PRELAB FOR EXTRASOLAR PLANETS
1. Explain the Doppler effect. Is a redshifted object moving
toward or away from us? What about a blueshifted object?
2. What is a light curve? 3. Approximately how many extrasolar
planets have been found to date? (Feel free to use the internet to
find this information, but make sure to reference your source).
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AST 113 – Summer 2009 Extrasolar Planets
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EXTRASOLAR PLANETS
What will you learn in this lab? We have developed models of the
solar system based on the mass, motions, locations, and
compositions of the planets and the Sun. Do other solar systems
exist? In this lab you will: • Categorize the properties of
terrestrial and Jovian planets in our solar system • Become
familiar with methods for looking for extrasolar planets • Use the
Braeside Observatory data to look for an extrasolar planet •
Determine whether other solar systems resemble our own
What do I need to bring to the Class with me to do this Lab? • A
copy of this lab script • Pencil and eraser • Scientific
Calculator
Introduction: In class, you have been studying properties of our
own solar system, learning about the Earth and Moon, other planets,
asteroids, comets, and meteorites, and the Sun. From your studies,
you have probably come to some conclusions as to how our solar
system works. Astronomers have developed models of how our solar
system formed based on our knowledge of the solar system. Are there
other solar systems? Do they look like ours? These are just a few
of the questions that astronomers are trying to answer. To do so,
we must scan the skies for other solar systems. To date, over 100
promising candidates for planets in orbit around other Sun-like
stars have been observed. These planets are called extrasolar
planets – implying that they orbit a star other than our own Sun.
There are two primary methods that astronomers have been using on
their search for extrasolar planets: Method 1: Doppler method In
your lecture course, you were introduced to the concept of Doppler
shifts – the perceived change in the frequency of light being
emitted by an object due to the relative motion between the object
and the observer. If the object is moving towards us, we see a
blueshift in the lines of the object's spectrum. Similarly, if the
object is moving away from us, we observe a redshift in the
object's spectrum.
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Figure 1:
Method 2: Transit method In your lecture course, you were
introduced to solar eclipses, where the Moon moves in front of the
Sun and blocks the sunlight from our perspective. The dimming light
from the Sun while being eclipsed can be plotted versus time,
resulting in a light curve. Figure 2:
In this lab exercise, you will use both methods to investigate
an extrasolar planet in orbit around a star very similar to our own
Sun. Write your answers to questions directly on the lab script and
have your TA check it off at the end of class. Exercise 1:
Properties of our own solar system
Because a star and its planets orbit a common center of mass, we
should observe Doppler shifts in the spectrum of the star. Figure 1
illustrates this process. The amount that a frequency of light is
shifted is proportional to the velocity of the planet in its orbit
around the star and mass of the planet tugging on the star.
Astronomers who are looking for extrasolar planets measure this
"wobble" by obtaining Doppler velocity curves. By using this
method, the mass and orbital semi-major axis for an extrasolar
planet may be obtained.
If an extrasolar planet orbits its star such that it passes
between the star and Earth, we observe an "eclipse" or transit. See
Figure 2 for an illustration of the transit and resulting light
curve. Astronomers are scanning the sky for stars that show
evidence of transits due to having planets in orbit. From a
transit, the radius of the planet may be calculated.
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The following table contains physical data for the nine planets
in our solar system.
Table 1 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Pluto
Semi-major axis (AU)
0.39 0.72 1.00 1.52 5.20 9.54 19.2 30.1 39.4
Mass (Earth masses – MEarth)
0.055 0.82 1.00 0.11 318 95.0 14.5 16.7 0.002
Radius (Earth radii - REarth)
0.38 0.95 1.00 0.53 11.2 9.5 4.0 3.7 0.19
Atmosphere none CO2/N N/O CO2/N H/He H/He H/He H/He ?
We divide the planets in the solar system into two major
classifications – Terrestrial (Earth-like) and Jovian
(Jupiter-like). By inspecting the values in Table 1, answer the
following questions.
1. Which four planets are terrestrial?
2. Which four planets are Jovian?
3. Which planet does not fit either category well?
4. Which type (terrestrial or Jovian) is more massive?
5. Which type (terrestrial or Jovian) has smaller radii?
6. Are the terrestrial planets located close to the Sun, far
from the Sun, or spread evenly throughout the entire solar
system?
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7. Are the Jovian planets located close to the Sun, far from the
Sun, or spread evenly throughout the entire solar system?
Exercise 2: Doppler Method In this section, we will use real
data from Doppler measurements of spectral lines in a star to
discover a planet orbiting the star and compare the results of the
discovery with planets in our solar system. Here is the Doppler
velocity curve for the star HD 209458. If the star did not have a
planet in orbit, the velocity would be constant (no redshift or
blueshift).
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8. Use information given on the graph to determine the period of
the planet's orbit, P, in days.
P = _______________ days
9. What is P in years? P = _______________ years
10. What is the amplitude of the curve (orbital velocity), K, in
m/s? (Take 1/2 of the full range of velocities.)
K = _______________ m/s
11. We will make some simplifying assumptions for this new
planetary system:
a. The orbit of the planet is circular (e = 0). b. The mass of
the star is 1 solar mass. c. The mass of the planet is much, much
less than that of the star. d. We are viewing the system nearly
edge on e. We express everything in terms of the mass and period of
Jupiter.
We make these assumptions to simplify the equations we have to
use for determining the mass of the planet. The equation we use is:
Mplanet = (P/12)
1/3 ! (K/13) ! MJupiter
P should be expressed in years and K in m/s. To compare to our
solar system, twelve years is the approximate orbital period for
Jupiter and 13 m/s is the magnitude of the "wobble" of the Sun due
to Jupiter's gravitational pull. Use your values for P and K and
calculate the mass of this new planet in terms of the mass of
Jupiter. Mplanet = ________________ MJupiter Recall that MJupiter =
318 MEarth Mplanet = ________________ MEarth
12. From our assumptions above, we can calculate the distance
(in AU) this planet is away from its star using Kepler's 3rd
law:
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a3/P2 = 1 using P in years. Solve for a, the semi-major axis, in
AU. a = ____________________ AU
13. Compare this planet to those in our solar system. Where is
its orbit located? (For example, if in our solar system, would this
planet lie between Mars and Jupiter?)
Exercise 3: Transit Method Now you will use observations of a
star from the Braeside Observatory to see if you can verify the
presence of a planet around this star using the transit method. The
Braeside telescope is a 16-inch telescope located in Flagstaff,
Arizona. Your instructor will provide you with a light curve of a
star that was made using observations from this telescope. Your
plot displays change in brightness of the star, !m and phase.
Looking at your plot,
answer the following questions.
14. During the given observation of _________(write name of
star), was a planet transiting the star? How can you tell?
If your Braeside data did indeed show a planet transiting, then
answer the following questions for that data. If not, then use the
light curve from the extrasolar planet transit over the star
HD209458 from Nyrola Observatory in Finland provided at the end of
this lab script.
15. What is the change in brightness, !m, of the star while the
planet is transiting?
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The change in brightness may be used to calculate the radius of
the planet. Specifically,
2
*
!!"
#$$%
&='r
rm
p
You will use the change in brightness that you calculated for
question 15 and assume that the radius of HD 209458 is similar to
our Sun's (radius of the Sun = 6.96 x 108 m). It would also be
useful to express the radius in terms of Jupiter radii (RJupiter)
to help give us a sense of size of the planet compared to planets
in our solar system. Accounting for these factors,
mrp
!= 8.9
16. What is the radius of the planet, rp (expressed in
RJupiter)?
17. What is the radius of the planet, rp (expressed in REarth)?
Questions:
18. Based on its distance from its parent star (calculated in
Exercise 2), would you call the planet around HD 209458 a
terrestrial or a Jovian planet?
19. Based on the mass that you calculated for the planet in
Exercise 2, would you call it a terrestrial or Jovian planet?
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20. Based on the radius that you calculated for the planet (in
Exercise 3), would you call it a terrestrial or Jovian planet?
21. Spectroscopic observations of this planet have noted that it
is surrounded by a layer of hydrogen (H). Based on this
observation, would you call this planet a terrestrial or Jovian
planet?
22. Would the planet orbiting the star HD 209458 conform to
observations based on our solar system alone? Why or why not?
23. Will the unusual characteristics of some of the extrasolar
planets (like the one above) affect our models of how solar systems
form? Why or why not?
References:
• Figure 1 - Astronomy Today, 4th
edition, Chaisson and McMillan, Prentice Hall, 2002 • Figure 2 –
Brown and Charbonneau,
http://www.hao.ucar.edu/public/research/stare/hd209458.html • The
Doppler velocity curve for HD 209458 was obtained from the website:
http://exoplanets.org
• The equation for the radius of the planet from the photometry
data is from Santoretti & Schneider, A&AS, 134, 553.
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